Wednesday, January 24, 2018

1/20 Fold and Cut II

Today started with an interesting whiteboard demo for the Problem of the Week.  This is a fairly straight forward combinatorics problem on a small 2^9 total set of possibilities. One of my students just went ahead and wrote a python program to brute force check for the answer.  While this won't work in a contest setting, I really like the use of computational math. If I had access to a computer lab and I knew everyone could program I'd love to do a whole session around the Project Euler. It would also make a really cool class structure to learn programming over a period of time.

But the other thought experiment this generated was what is the purpose of some of these problems in the age of cheap computing?  This is well trod territory.  Open Middle problems as they are commonly formulated often make me think this is better done as a brute force search.

My current thinking is that computational math is more interesting if its quicker to write a program than a formal method or if essentially you need to search a wide domain for the answers and there isn't much structure to help out.  Also problems can be modified to make the computational requirements more interesting. But this is obviously a fuzzy standard and I'm not sure how to align this with my general ambivalence about calculators.

The problem was also an opportunity to hand out some geeky stickers I bought on a lark from https://mathsgear.co.uk/.    As an aside I went back and forth if the black sticker at the bottom should be read "No change in learning (bad) or peak learning (good)"

For the main activity, I've been meaning to do another day focusing on the Fold and Cut Theorem since it went so well two years ago.  At this point I only have 3 or 4 kids left from that time and I thought I could provide enough different tasks and/or they had not reached the end the first time that it wouldn't be boring for them.

This time around I went with a part of Erik Demaine's lecture  @ MIT.

The choice was motivated by the fact Demaine developed a lot of the algorithms and includes some historical notes on the first examples in Japan.  But also I'm terrible at folding and there are a bunch of great demos in the first 10 minutes which the kids really liked. That saved me from a lot of practice at home.

I paused at around the 9 minute mark and handed out worksheets I've used before from Joel Hamkins:
http://jdh.hamkins.org/math-for-nine-year-olds-fold-punch-cut/

These work great even for older kids.  While circulating I just made sure to periodically have everyone throw out their scrap paper and to emphasize the role of symmetry in any of the solutions.

(Some handiwork)

Finally I reserved 10 minutes at the end to go further in the video and watch the explanation of the straight-skeleton method.

P.O.T.W:

Another slightly modified AMC problem.

In 1998 the population of a town was a perfect square. Ten years later, after an increase of 150 people,
the population was 9 more than a perfect square. Now in 2018, with an increase of another 150 people
the population is once again a perfect square.  What was the population in all three years?

Planning:

MathCounts Prep 1/30